The crash on Sunday night caused a big explosion and toppled the structure, Whitmire said at a late-night press conference.
"The residents are secure and safe, but we have a terrible accident scene," Whitmire said.
The dead were onboard a privately owned Robinson R44 helicopter, reports Xinhua news agency, quoting Houston Police Chief Noe Diaz.
"This is a tragic event tonight. It's a tragic loss of life," Diaz said.
The mayor said the helicopter had departed from Ellington Airport with its destination unknown.
The victim identities were not immediately disclosed as an investigation into the crash is underway.